Looking for advice on best use of a large profit on the sale of a home.

We sold a home and currently have $160k cash surplus.
No consumer debt other than one car loan at $400 per month.
Our new mortgage is $2455 a month on a 15 year fixed (we put 20% down).
There is a total of $250k of school loans that we can refi (current offer with Sofi is a 10 year fixed at 4.5% at $2486 per month).
Income is $350k per year.
We had a great employer match at the last job, and total retirement/investments are $290k.
Current employer has no 401 for first year, so we plan to backdoor into Roth this year.

What is the best use of the $160 profit? Put some or all towards student loans? Keep the majority liquid in savings/investment accounts for emergency funds? Other suggestions? We are not risk adverse or debt adverse, but just trying to figure what is the best option.

You will only know "best" for sure in hindsight. Reasonable cases can be made for any of the options you listed (e.g., pay student loans or invest in stocks), except perhaps for a $160K emergency fund (seems a bit much).